# Topological Trajectory Classification with Filtrations of Simplicial Complexes and Persistent Homology

Florian T. Pokorny, Majd Hawasly, Subramanian Ramamoorthy
In International Journal of Robotics Research (IJRR), 2016

## Abstract

In this work, we present a sampling-based approach to tra- For robots to autonomously operate in a wide variety of jectory classification which enables automated high-level reasoning about topological classes of trajectories. Our approach is applicable to general configuration spaces and relies only on the availability of collision free samples. Unlike previous sampling-based approaches in robotics which use graphs to capture information about the path-connectedness of a configuration space, we construct a mul- tiscale approximation of neighborhoods of the collision free configurations based on filtrations of simplicial complexes. Our approach thereby extracts additional homological information which is essential for a topological trajectory classifi- cation. We propose a multiscale classification algorithm for trajectories in configuration spaces of arbitrary dimension and for sets of trajectories starting and ending in two fixed points. Using a cone construction, we then generalize this approach to classify sets of trajectories even when trajectory start and end points are allowed to vary in path-connected subsets. We furthermore show how an augmented filtration of simplicial complexes based on an arbitrary function on the configuration space, such as a costmap, can be defined to incorporate additional constraints. We present an evaluation of our approach in 2, 3, 4 and 6 dimensional configuration spaces in simulation and in real-world experiments using a Baxter robot and motion capture data.

## Bibtex

@article{pokorny2016c, author = {Pokorny, Florian T. and Hawasly, Majd and Ramamoorthy, Subramanian}, title = {Topological Trajectory Classification with Filtrations of Simplicial Complexes and Persistent Homology}, journal = {International Journal of Robotics Research (IJRR)}, year = {2016}, }